You will be paying $$12,000$ a year in tuition expenses at the end of the next two years. Bonds currently yield $9\%.$

Required:

a$.$ What are the present value and duration of your obligation? $($Do not round intermediate calculations. Round "Present

value" to $2$ decimal places and "Duration" to $4$ decimal places.$)$

b$.$ What is the duration of a zero$-$coupon bond that would immunize your obligation tand its future redemption value? $($Do

not round intermediate calculations. Round "Duration" to $4$ decimal places and "Future redemption value" to $2$ decimal

places.$)$

c$.$ Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates

immediately increase to $10\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond

and that of your tuition obligation? $($Enter your answer as a positive value. Do not round intermediate calculations.

Round your answer to $2$ decimal places.$)$

Net position changes by

d$.$ Suppose you buy a zero$-$coupon bond with value and duration equal to your obligation. Now suppose that rates

immediately falls to $8\%.$ What happens to your net position, that is$,$ to the difference between the value of the bond and

that of your tuition obligation? $($Enter your answer as a positive value. Do not round intermediate calculations. Round

your answer to $2$ decimal places.$)$